Dot Product Bounds in Galois Rings

2022/07/20 by David L. Crosby, Crosby, David · 1 citation
Computer Science · Mathematics · #11T24 (Secondary) #51A20 (Primary) #52C10 (Secondary) #Coding theory and cryptography #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Metric Geometry (math.MG) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2207.10051

openalex publication_date 2022/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a problem related to the Erdoős Unit Distance Conjecture: How often can a single dot product configuration or a multiple dot product configuration occur over a Galoi Ring? We also find a bound on an inverse vector matrix multiplication problem.

Cited by

• A Density Condition on Point Sets with Slowly-Scaling Distinct Dot Products

Related

• Pairs of dot products in finite fields and rings
• On the number of dot product chains in finite fields and rings
• Dot product chains
• Geometric configurations in the ring of integers modulo p^ℓ
• Bounds on point configurations determined by distances and dot products